Cumulative hierarchy
id:
cumulative-hierarchy-263-5190970
title:
Cumulative hierarchy
text:
In mathematics, specifically set theory, a cumulative hierarchy is a family of sets W α indexed by ordinals α such that W α ⊆ W α + 1 If λ is a limit ordinal, then W λ = ⋃ α < λ W α Some authors additionally require that W α + 1 ⊆ P or that W 0 ≠ ∅ . The union W = ⋃ α ∈ O n W α of the sets of a cumulative hierarchy is often used as a model of set theory. The phrase "the cumulative hierarchy" usually refers to the standard cumulative hierarchy V α of the von Neumann universe with V α + 1 = P intr
brand slug:
wiki
category slug:
encyclopedia
description:
Family of sets indexed by ordinal numbers
original url:
https://en.wikipedia.org/wiki/Cumulative_hierarchy
date created:
date modified:
2022-07-06T09:54:07Z
main entity:
{"identifier":"Q18349448","url":"https://www.wikidata.org/entity/Q18349448"}
image:
fields total:
13
integrity:
14